Chapter 10, Problem 22A

Paula flies a loop-the-loop maneuver at constant speed. Two forces act on Paula, the force due to gravity and the normal force of the seat pressing on her (which provides the sensation of weight). Rank from largest to smallest the normal forces on Paula at points A, B, and C.

To determine

To rank: The normal forces acting on Paula from largest to smallest.

Answer to Problem 22A

  $A>B>C$

Explanation of Solution

Introduction:

An object stays in a circular motion due to centripetal force acting on it. Centripetal force is the force that acts towards the centre of the circular path covered by the object.

Since the normal force and the force due to gravity are always equal and opposite to each other, so it can be concluded that the normal force will be equal to the weight of the object but it acts in the opposite direction. In the given case, at point A, the normal force will be maximum because the position is upright and at point B, the loop maneuver is facing upwards changing the position such that the weight will be lesser as compared to the weight at point A, hence the normal force is lesser. At point C, now the position of the loop maneuver is upside down making the weight even less than the previous cases. Hence, the normal force will be less in case of C.

So, the ranking on the basis of normal forces acting on Paula can be given by:

  $A>B>C$

Conclusion:

Hence, the ranking is given as $A>B>C$ .